Ultimate Card Tracking Challenge.
February 14th, 2013 at 6:57:46 PM
permalink
Ultimate BJ card tracking challenge.
---------------------------------
8 decks of cards stand before you- all 32 of the Aces are at the bottom of the stack of 416 cards.
The decks are shuffled by hand using the typical technique. The riffle/splits/cuts/boxing/shuffles are all done perfectly in halves and one card from each hand at a time. riffling has the dealers left hand/card go down first before the following card from the right hand. splits/cuts the top half goes to the right hand. Any rounding of cards stays with the original stack/bottom.
The 416 cards are split into two stacks with the top to the right of the bottom half.
Each half is then split into 1/3rds- 69 cards, 69 cards, and 70.
Each third is grabbed in 1/4th of a deck groups (13 cards) the left thirds stacked onto each other and the right 1/3rd stacked onto each other so that the dealer riffles 39 cards from the right half and 39 cards from the left half into each other at once. (just as video shows it being done- grabbing from the 1/3rd that came from the top-most position of the original stack first, and laying that on top of the 13 cards from the next stack, and then the 13 cards from the stack that was originally closest to the bottom last- placing that 13 cards under the other 26... see video. ;)
**Very important note- doing 13 cards at a time out of 69 leaves 4 left over (and 5 left over on the bottom/1st third)- DO A SMALL SHUFFLE OF THE LEFTOVER AMOUNTS FIRST- the top 4-4-5 from each side's thirds so that 65 cards remain in each of your 6 stacks- this was done first so that the rest would be even and so you could actually have a hope to track the cards. So the very first riffle contains 13 cards in each hand (26 total) and then is boxed in 1/4s with the remainder staying on the last/bottom 1/4 as noted at the beginning. After this initial small size riffle youd go to riffling a full 78 cards at once)
The resulting shuffled cards are then boxed into 1/4ths- taking the top 19 to the bottom, the next 19, the next 19 and then the final 21 cards are moved to the top.
the process is repeated until all 6 groups are cards are reshuffled into one stack.
The new stack of cards is split in half. again the top half is to the right of the bottom half. The half on the right is cut in half and restacked.
The resulting two stacks of cards- (208 each) are now riffled together one final time in the form of taking a half deck amount of cards from each stack (26 cards each at a time) and shuffling into a new single stack.
When all cards have been shuffled in this way one last cut is made to the deck of cards- 2/3rd of the way down the stack (the top 276 cards are now the bottom 276 cards).
Where are the Aces now? In places from the top of the deck. (first card off top is 1st position, last card on bottom is 416th)
Here is a video that illustrates the process. Just remember in my account/question everything is done perfectly and all the decks are even with the rounded number of cards going to the bottom.
NOTES WITH VIDEO:
1) don't concern about the plugging- watch video from 1:26 onward.
2) the video does not illustrate the top half of the deck being cut at the halfway point and restacked- this would have occurred at 6:35 before the final shuffling of the cards.
http://youtu.be/9YXljS36yD0?t=1m26s
=========================================
Ill give you credit if you can even tell me where ONE of the Aces are- and full credit if you can tell me where all 32 Aces are.
I figured I would put this in the math section because you should be able to do the calculations in a mathematical way. So long as you catch/understand al the restrictions and noted exceptions. Clarification or anything needed ask- Ill try to answer best I can.
---------------------------------
8 decks of cards stand before you- all 32 of the Aces are at the bottom of the stack of 416 cards.
The decks are shuffled by hand using the typical technique. The riffle/splits/cuts/boxing/shuffles are all done perfectly in halves and one card from each hand at a time. riffling has the dealers left hand/card go down first before the following card from the right hand. splits/cuts the top half goes to the right hand. Any rounding of cards stays with the original stack/bottom.
The 416 cards are split into two stacks with the top to the right of the bottom half.
Each half is then split into 1/3rds- 69 cards, 69 cards, and 70.
Each third is grabbed in 1/4th of a deck groups (13 cards) the left thirds stacked onto each other and the right 1/3rd stacked onto each other so that the dealer riffles 39 cards from the right half and 39 cards from the left half into each other at once. (just as video shows it being done- grabbing from the 1/3rd that came from the top-most position of the original stack first, and laying that on top of the 13 cards from the next stack, and then the 13 cards from the stack that was originally closest to the bottom last- placing that 13 cards under the other 26... see video. ;)
**Very important note- doing 13 cards at a time out of 69 leaves 4 left over (and 5 left over on the bottom/1st third)- DO A SMALL SHUFFLE OF THE LEFTOVER AMOUNTS FIRST- the top 4-4-5 from each side's thirds so that 65 cards remain in each of your 6 stacks- this was done first so that the rest would be even and so you could actually have a hope to track the cards. So the very first riffle contains 13 cards in each hand (26 total) and then is boxed in 1/4s with the remainder staying on the last/bottom 1/4 as noted at the beginning. After this initial small size riffle youd go to riffling a full 78 cards at once)
The resulting shuffled cards are then boxed into 1/4ths- taking the top 19 to the bottom, the next 19, the next 19 and then the final 21 cards are moved to the top.
the process is repeated until all 6 groups are cards are reshuffled into one stack.
The new stack of cards is split in half. again the top half is to the right of the bottom half. The half on the right is cut in half and restacked.
The resulting two stacks of cards- (208 each) are now riffled together one final time in the form of taking a half deck amount of cards from each stack (26 cards each at a time) and shuffling into a new single stack.
When all cards have been shuffled in this way one last cut is made to the deck of cards- 2/3rd of the way down the stack (the top 276 cards are now the bottom 276 cards).
Where are the Aces now? In places from the top of the deck. (first card off top is 1st position, last card on bottom is 416th)
Here is a video that illustrates the process. Just remember in my account/question everything is done perfectly and all the decks are even with the rounded number of cards going to the bottom.
NOTES WITH VIDEO:
1) don't concern about the plugging- watch video from 1:26 onward.
2) the video does not illustrate the top half of the deck being cut at the halfway point and restacked- this would have occurred at 6:35 before the final shuffling of the cards.
http://youtu.be/9YXljS36yD0?t=1m26s
=========================================
Ill give you credit if you can even tell me where ONE of the Aces are- and full credit if you can tell me where all 32 Aces are.
I figured I would put this in the math section because you should be able to do the calculations in a mathematical way. So long as you catch/understand al the restrictions and noted exceptions. Clarification or anything needed ask- Ill try to answer best I can.
"Although men flatter themselves with their great actions, they are not so often the result of a great design as of chance." - Francois De La Rochefoucauld
